text:
\section{Introduction}
\label{sec:intro}

It is well established that dark matter makes up about $85\%$ of the mass in the Universe~\cite{Ade:2015xua}. Indirect searches of high-energy standard model particles originating from dark matter annihilations or decays provide an important way of understanding its nature. Of central importance to the indirect detection search is the distribution of dark matter within galactic halos. In the prevailing scenario of dark matter, it is composed of collisionless thermal relics. Numerical simulations show that collisionless dark matter (CDM) typically produces a Navarro-Frenk-White (NFW) density profile in the halo~\cite{Navarro:1995iw,Navarro:1996gj}, which has a characteristic feature of $\rho(r)\propto r^{-1}$ towards the center~\cite{Dubinski:1991bm}. It has also been established that virtually all large galaxies host central supermassive black holes, see, e.g.~\cite{Kormendy:2013dxa}. The presence of a central black hole could alter the dark matter density profile in the inner halo, and for the standard NFW profile a density spike, $\rho(r)\propto r^{-7/3}$, could form near a black hole that grew adiabatically~\cite{Gondolo:1999ef}. The high density of the spike could boost the dark matter annihilation rate. For example, the Milky Way hosts a central supermassive black hole with mass $\sim4\times10^6~{\rm M_\odot}$~\cite{Gillessen:2008qv,Ghez:2008ms}. Dark matter annihilations could produce very bright sharp signals that may be visible as a point source in the galactic center, see, e.g.,~\cite{Gondolo:1999ef,Hooper:2002ru,Aloisio:2004hy,Fields:2014pia,Belikov:2016fwv,Sandick:2016zeg,Chiang:2019zjj}.

It's less known observationally whether small dwarf galaxies, like satellite galaxies of the Milky Way, may host central black holes with intermediate masses. Interestingly, one could derive constraints on the central black hole mass in the satellites using dark matter indirect detection observations. For example, for the thermal relic scenario with an $s$-wave annihilation cross section, the central black hole mass cannot be higher than $\sim10^2\textup{--}10^3~{\rm M_\odot}$ in Draco~\cite{Wanders:2014xia}, the most dense satellite of the Milky Way, otherwise the flux of dark matter annihilation signals would surpass the upper limit from Fermi-LAT gamma-ray observations due to the presence of the density spike induced by the black hole. The limit could be relaxed if the power law of the spike is more mild. This could occur if the black hole grows away from the center of the halo or it does not grow adiabatically from a seed, but being brought in by mergers~\cite{Ullio:2001fb}. In addition, mergers of black holes in the centers of the progenitor halos could erase the density spike~\cite{Merritt:2002vj}. Gravitational scatterings between stars and dark matter particles could also kinetically heat up the spike and reduce its density~\cite{Gnedin:2003rj,Merritt:2003qk}.

In this work, we study the dark matter distribution near a black hole in self-interacting dark matter (SIDM), see~\cite{Tulin:2017ara} for a recent review. In this scenario, dark matter has strong self-interactions that can thermalize the inner halo over cosmological timescales~\cite{Dave:2000ar,Vogelsberger:2012ku,Rocha:2012jg,Peter:2012jh,Zavala:2012us,Vogelsberger:2015gpr,Fischer:2020uxh}. Recent studies show that SIDM is favored for explaining diverse dark matter distributions over a wide range of galactic systems~\cite{Kaplinghat:2015aga,Kamada:2016euw,Creasey:2016jaq,Ren:2018jpt,Kaplinghat:2019svz,Sameie:2019zfo,Kahlhoefer:2019oyt,Yang:2020iya,Sagunski:2020spe,Andrade:2020lqq}, implying that the inner region of dark halos might be indeed thermalized. We assume that dark matter particles follow an isothermal distribution, which is well justified for SIDM halos, and show that a central black hole induces a density spike with the power law $\rho(r)\propto r^{-3/2}$; see also~\cite{Gondolo:1999ef}. If dark matter annihilations occur, a weak density cusp could form with $\rho(r)\propto r^{-1/2}$ within the spike as in the CDM case. We apply these results to Draco and derive Fermi-LAT gamma-ray constraints on the annihilation cross section for both SIDM and CDM halo models, inferred from fits to stellar kinematic data of Draco~\cite{Kaplinghat:2019svz}. For the SIDM halo, the predicted signal flux is insensitive to the black hole mass unless it is larger than $\sim10^{7}~\rm{M_{\odot}}$, which is unlikely for dwarf galaxies like Draco. Thus, the satellites of the Milky Way could contain central black holes with intermediate masses $\sim600~{\rm M_\odot}$ as expected in the black hole-host galaxy relation~\cite{Tremaine:2002js}, while their host halos are still composed of thermal relic dark matter. We will further show that observations from the M87  galaxy, which hosts a supermassive black hole, do not generally exclude thermal relic dark matter for SIDM, in contrast to the CDM case~\cite{Lacroix:2015lxa,Lacroix:2016qpq}. Interestingly, M87 remains a promising target for probing the SIDM spike for light dark matter with data from the Event Horizon Telescope.

The rest of the paper is organized as follows. In Sec. II, we introduce the SIDM halo model and calculate profiles for dark matter spikes. In Sec. III, we derive Fermi-LAT constraints on the annihilation cross section and the black hole mass for Draco. In Sec. IV, we discuss implications for M87. We conclude in Sec. V.

\section{Isothermal SIDM Spikes and Weak Annihilation Cusps}

\begin{figure}[t!]
\includegraphics[scale=0.35]{density}
\caption{normalized density profiles for isothermal SIDM halos near a black hole for two different values of the 1D velocity dispersion. For the region outside the annihilation radius $r \gg r_{\rm{ann}}$, the density profiles follow a power law of $r^{-3/2}$. Inside the annihilation cusp, $\rho(r)\propto r^{-1/2}$. If dark matter does not annihilate, the density could increase exponentially towards the black hole (dashed). }
\label{fig:Density}
\end{figure}

Since strong dark matter self-interactions can erase velocity anisotropies as demonstrated in N-body simulations, see, i.e.,~\cite{Vogelsberger:2012sa}, we assume dark matter particles in the inner SIDM halo follow an isotropic phase space distribution $f(E)$ and write the density profile $\rho(r)$ as
\begin{equation}
\label{eq:density_def}
\rho(r) = \int d^{3}v f(E)=4 \pi \int_{0}^{v_{\rm{esc}}} dv v^{2} f(E) \ ,
\end{equation}
where $E$ is the energy per unit mass and $v_{\rm esc}$ is the escape velocity. For the region where the gravitational potential is dominated by a black hole, we have $E=v^{2}/2 - G M_{\bullet}/r$, where $M_{\bullet}$ is the black hole mass. We only consider the contribution of dark matter particles gravitationally bound to the black hole and integrate the velocity up to the escape velocity $v_{\rm{esc}}=\sqrt{2GM_{\rm{\bullet}} / r}$.

We further assume that the phase space distribution follows an isothermal distribution, as dark matter collisions thermalize the inner halo. We expect this is a good approximation as long as the radius is larger than the horizon size of the black hole $2 {G M_{\bullet}}/c^2$, around which the relativistic effect becomes important and the isothermal assumption breaks down due to the curvature effect of space-time~\cite{Shapiro:2014oha,Shapiro:2018vju}. In the region where the black hole dominates the potential, we have
\begin{equation}
\label{eq:phase_space_def}
f(E)=\frac{\rho_{0}}{(2 \pi \sigma_{0}^{2})^{3/2}} e^{-E/\sigma_{0}^{2}}=\frac{\rho_{0} e^{G M_{\bullet}/r \sigma_{0}^{2}}}{(2 \pi \sigma_{0}^{2})^{3/2}} e^{-\frac{1}{2} v^{2} / \sigma_{0}^{2}}
\end{equation}
where $\rho_{0}$ is a normalization and $\sigma_{0}$ is the one dimensional velocity dispersion.
Inserting Eq. \ref{eq:phase_space_def} into Eq. \ref{eq:density_def} and performing the integral, we obtain the density profile
\begin{equation}
\label{eq:density_solution_0}
\rho (r) = \rho_{0} \left [ e^{r_{\rm{H}} / r} {\rm erf} \left (\frac{r_{\rm bh}}{r} \right)-2\sqrt{\frac{r_{\rm{bh}}}{\pi r}} \right ],
\end{equation}
where $r_{\rm{bh}} = G M_{\rm{\bullet}} / \sigma_{0}^{2}$ characterizes the black hole's sphere of influence and ${{\rm erf}(x)}$ is the error function. In the limit $r \gg r_{\rm{bh}}$, Eq. \ref{eq:density_solution_0} leads to a scaling relation of $\rho(r)\propto r^{-3/2}$, which is much shallower than the spike profile predicted in the NFW halo model, $\rho(r)\propto r^{-7/3}$.

We note the derivation presented above is similar to the one in~\cite{Gondolo:1999ef}, which takes the isothermal halo model as an example for case studies. However, in the collisionless limit, dark matter particles do not generally follow an isothermal distribution. Ref.~\cite{Gnedin:2003rj} proposes that frequent gravitational scatterings between stars near the black hole and dark matter particles could drive the latter to follow an isothermal distribution. This could be the case in the galactic center of the Milky Way, as it harbors a compact cluster of stars near the black hole with extremely high stellar density, $8\times10^8~{\rm M_\odot/pc^3}$~\cite{Genzel:2003cn}, and the scattering rate is high accordingly. It's not clear whether this mechanism holds for satellite galaxies of the Milky Way on which we will mainly focus later. Unlike the Milky Way, the stellar component is negligible dynamically in the center of the satellites. Even if they host an intermediate mass black hole at the center, the stellar density near the hole may not be high enough for sufficient star-dark matter interactions. On the other hand, in SIDM, dark matter particles in the inner halo follow an isothermal distribution, and it naturally predicts a weaker density cusp near a black hole, compared to CDM.

For $r \ll r_{\rm{bh}}$, the density profile given in Eq.~\ref{eq:density_solution_0} begins to diverge exponentially. However, dark matter annihilations can deplete dark matter particles in the high density regions and change the profile accordingly, resulting in an weak annihilation cusp~\cite{Vasiliev:2007vh,Shapiro:2016ypb}. Consider the annihilation radius $r_{\rm{ann}}$ that defines the onset of the annihilation cusp where the density is high enough such that the dark matter annihilation rate becomes once per age of the black hole,
\begin{equation}
\label{eq:ann_density_def}
\rho (r_{\rm{ann}}) = \frac{m_{\chi}}{\left < \sigma_{\rm{ann}} v \ \right > t_{\rm age}}
\end{equation}
where $\left < \sigma_{\rm{ann}} v \ \right >$ is the thermally averaged annihilation cross section, $m_{\chi}$ is the dark matter mass and $t_{\rm age}$ is the age of the black hole. When calculating the dark matter density in the presence of annihilations, we make the simplification that if a particles orbit is entirely within the annihilation cusp, it has annihilated within the age of the black hole and does not contribute to the final density. On the other hand, if the particle's orbit carries it outside the annihilation cusp at any point, then it has completely escaped annihilations. We require that $v_{\rm{ann}}$ be the minimum velocity necessary such that the particles orbit reach $r_{\rm{ann}}$,
\begin{equation}
\label{eq:ann_velocity_def}
v_{\rm{ann}}=\sqrt{2GM_{\rm{\bullet}}} \left ( \frac{1}{r}-\frac{1}{r_{\rm{ann}}} \right )^{\frac{1}{2}}.
\end{equation}
We derive Eq. \ref{eq:ann_velocity_def} by setting the energy equal to the gravitational potential at the annihilation radius, $E = - G M_{\bullet} / r_{\rm{ann}} $, and solving for the velocity $v_{\rm ann}$. Hence, the density integral for an isothermal distribution including annihilations is $\rho(r)=4\pi\int^{v_{\rm esc}}_{v_{\rm low}}dv v^2 f(E)$, where $v_{\rm low}=0$ for $r>r_{\rm ann}$, and $v_{\rm ann}$ for $r<r_{\rm ann}$. We find the density profile as
\begin{equation*}
\label{eq:density_solution}
\rho (r) = \rho_{0} \times \begin{cases}
e^{r_{\rm bh} / r} {\rm erf} \left ( \sqrt{\frac{{r}_{\rm{bh}}}{r}} \ \right )-2\sqrt{\frac{r_{\rm bh}}{\pi \mathit{r}}}, r \geq r_{\rm{ann}} \\
e^{r_{\rm bh} / r} \left [ {\rm erf} \left ( \sqrt{\frac{r_{\rm bh}}{r}}  \right ) - {\rm erf} \left ( \sqrt{\frac{r_{\rm bh}}{r} - \frac{r_{\rm bh}}{r_{\rm ann}}} \right ) \right ] - 2 \left [ \sqrt{\frac{r_{\rm bh}}{\pi r}} - \sqrt{\frac{r_{\rm bh}}{\pi r} - \frac{r_{\rm bh}}{\pi r_{\rm ann}}} e^{r_{\rm bh} / r_{\rm ann}} \ \right ], r< r_{\rm ann}.
\end{cases}
\end{equation*}
In the limit $r\ll r_{\rm ann}<r_{\rm{bh}}$, $\rho(r)\approx(2\rho_0/\sqrt{\pi})[\exp(r_{\rm bh}/r_{\rm ann})-1]\sqrt{r_{\rm bh}/r}$. Thus, we find for the SIDM density profile within the annihilation cusp follows a a weak cusp power law $r^{-1/2}$. Interestingly, this result is also generic for any phase space distribution which can be written in terms of power laws in $E$. Suppose that $f(E) \sim \left | E \ \right |^{p}$ then for any power $p$ the $r \ll r_{\rm ann} $ behavior results in a $r^{-1/2}$ weak cusp power law~\cite{Vasiliev:2007vh,Shapiro:2016ypb}.

Fig.~\ref{fig:Density} shows the normalized density profile for different values of $\sigma_{0}$. When including annihilations a weak cusp is clearly visible. It is clear that for any $\sigma_{0}$ the $r \ll r_{\rm{ann}}$ behavior corresponds with the $r^{-1/2}$ weak cusp power law. Similarly, the $r \gg r_{\rm{ann}}$ behavior shows a $r^{-3/2}$ power law across varying $\sigma_{0}$. Near the annihilation radius if $ \sigma_{0}^{2} < G M_{\rm{\bullet}} / r_{\rm{ann}}$, an exponential spike in the dark matter density can develop. The weak cusp power law $\rho(r) \propto r^{-1/2}$ is a feature which is present in both SIDM and CDM halo models, although their spike profiles are different. In the extreme inner regions of the halo near the black hole, the available phase space is altered by the presence of a loss cone~\cite{Shapiro:2016ypb}, i.e, if a dark matter particle orbit brings it too close to the horizon radius then it will get absorbed by the black hole. We do not consider those effects in this work, because they do not affect our main results.

\section{Applications to Draco}

\begin{figure}[t!]
\includegraphics[scale=0.35]{draco1}\;\;
\includegraphics[scale=0.35]{draco2}
\caption{{\it Left:} dark matter halo density profiles for isothermal SIDM (red) and CDM (black) halo models for the Milky Way satellite galaxy Draco without (solid) and with (dashed) a central black hole. For the latter case, the black hole mass is assumed to be $10^{5}~{\rm M_{\odot}}$ and the density spike follows a power law of $r^{-3/2}$ and $r^{-7/3}$ for the SIDM and CDM halos, respectively. A steep cutoff at around $10~{\rm kpc}$ is due to tidal stripping. {\it Right:} upper limits on the annihilation cross section vs. the central black hole mass for the SIDM (red) and CDM (black) halos with density spikes, based on Fermi-LAT gamma-ray observations of Draco. The dark matter mass is $10~{\rm GeV}$ (dashed) and $1~{\rm TeV}$ (solid). The horizontal line denotes the canonical thermal annihilation cross section (gray dotted).}
\label{fig:draco}
\end{figure}

The presence of dark matter spikes could significantly boost indirect detection signals. In turn, if we assume dark matter is made of thermal relics, we can derive constraints on the mass of central black holes of galaxies using results from dark matter indirect searches. Ref.~\cite{Wanders:2014xia} considers Draco, the most dense satellite of the Milky Way, and shows its black hole mass cannot be larger than $10^2\textup{--}10^3~{\rm M_{\odot}}$ for the dark matter mass in the range $100~{\rm GeV}\textup{--}1~{\rm TeV}$, based on the Fermi-LAT gamma-ray data.

Since the SIDM halo model predicts a much shallower density spike than the CDM one, we expect that the upper limits on $M_\bullet$ for Draco could be relaxed if its inner halo is thermalized due to dark matter self-interactions. To see the difference, we first consider dark matter density profiles for Draco without a black hole. Ref.~\cite{Kaplinghat:2019svz} fits the line-of-sight stellar velocity dispersion of Draco with an NFW profile and finds the best-fit values of the scale density and radius are $\rho_s\approx1.68\times10^{7}~{\rm M_\odot/kpc^3}$ and $r_s\approx1.94~{\rm kpc}$, respectively. In addition, it also considers a cored isothermal density profile following the solution to the Jeans equation $\sigma^2_0\nabla^2\ln\rho=-4\pi G\rho$ with the boundary conditions $\rho(0)=\rho_0$ and $\rho'(0)=0$, and finds the best fit values $\rho_0\approx2.55\times10^8$ and $\sigma_0\approx13.88~{\rm km/s}$. This isothermal profile was first proposed to model dark matter distributions in an inner SIDM halo~\cite{Kaplinghat:2015aga,Kaplinghat:2013xca} and it agrees with N-body simulations remarkably well~\cite{Robertson:2017mgj,Ren:2018jpt,Robertson:2020pxj}. The left panel of Fig.~\ref{fig:draco} (solid) shows the dark matter density profiles for Draco inferred from fitting to stellar kinematics as in~\cite{Kaplinghat:2019svz}, where we have extrapolated them for $r\gtrsim10~{\rm kpc}$ using a power law of $r^{-5}$ to account for tidal stripping.

To see the influence of a central black hole in Draco, we determine the radius of influence through the condition~\cite{Merritt:2003qk}
\begin{equation}
\label{eq:mass}
4\pi \int_{0}^{r_{\rm bh}}dr r^{2} \rho(r) = 2 {M_{\bullet}},
\end{equation}
which indicates the region where the black hole mass dominates. We use $\rho_{\rm{spike}}(r) = \rho(r_{\rm spike}) \left ( r_{\rm{spike}} / r \right )^{\gamma}$ to model the spike density profile, where the spike radius is given by $r_{\rm{spike}}\approx0.2 r_{\rm{bh}}$~\cite{Merritt:2003qc}. The spike scaling is given by $\gamma=3/2$ and $7/3$ for the SIDM and CDM halos, respectively. Taking $M_{\bullet}=10^{5}~{\rm M_\odot}$ as an example, we find $r_{\rm bh}\approx4.7\times10^{-2}~{\rm kpc}$, hence $r_{\rm spike}\approx9.3\times10^{-3}~{\rm kpc}$ and $\rho(r_{\rm spike})\approx2.4\times10^8~{\rm M_\odot/kpc^3}$ for the SIDM halo shown in the left panel of Fig.~\ref{fig:draco}. For the CDM halo, $r_{\rm spike}\approx3.7\times10^{-3}~{\rm kpc}$ and $\rho(r_{\rm spike})\approx8.3\times10^9~{\rm M_\odot/kpc^3}$. The dashed curves in the left panel of Fig.~\ref{fig:draco} denote the spike profiles. Note the annihilation radius is much smaller than the spike radius and we do not show it in the figure. For instance, consider $\left<\sigma_{\rm ann}v\right>=3\times10^{-26}~{\rm cm^3/s}$ and $m_\chi=100~{\rm GeV}$, we find $r_{\rm ann}\approx10^{-9}~{\rm kpc}$ and $10^{-7}~{\rm kpc}$ for the SIDM and CDM halos, respectively.

We consider dark matter annihilations to ${b\bar{b}}$ states, which further produce gamma-ray signals. The differential flux from the contribution of the smooth halo component can be calculated as
\begin{equation}
\label{eq:halo}
\frac{d \Phi_{\rm{halo}}}{dE} = \frac{1}{2} \frac{\left <  \sigma_{\rm{ann}} v \right >}{4 \pi m_{\chi}^{2}} \frac{d N}{ dE} \bar{J}
\end{equation}
where $dN/dE$ is the photon spectrum and $\bar{J}$ is the angular integrated $J$ factor given by
\begin{equation}
\bar{J}=2\pi\int^{\theta_{\rm{max}}}_{0} d\theta\sin\theta J(\theta)= 2\pi\int^{\theta_{\rm{max}}}_{0}d\theta \sin\theta \int_{l.o.s} ds \rho^{2}[r(\theta,\rm{s})].
\end{equation}
To perform the integral along the line of sight direction, we write $r(s,\theta) = \sqrt{D^2 + s^{2} - 2 s D  \cos(\theta)}$, where $D\approx76~{\rm kpc}$ is the distance from Earth to Draco, and we set $\theta_{\rm max}=0.5^{\rm o}$, corresponding to a solid angle of $2.4\times10^{-4}~{\rm sr}$. For the SIDM and CDM halos of Draco shown in the left panel Fig.~\ref{fig:draco} (solid), we find $\bar{J}\approx5.0\times10^{18}~{\rm GeV^2/cm^5}$ and $4.8\times10^{18}~{\rm GeV^2/cm^5}$, respectively. We see that although the two halo models have very different inner density profiles, their $\bar{J}$ factors are similar.

For the contribution from the density spike, we have
\begin{equation}
\label{eq:spike}
\frac{d\Phi_{\rm{spike}}}{dE} = \frac{1}{2} \frac{\left < \sigma_{\rm{ann}} v \right >}{m_{\chi}^{2}D^{2}} \frac{dN}{dE} Q,
\end{equation}
where the $Q$ factor is calculated as
\begin{equation}
\label{eq:qfactor}
Q=\int_{r_{\rm ann}}^{{r_{\rm spike}}} dr r^{2} \rho_{\rm{spike}}^{2}(r)=
\begin{cases}
\rho^2(r_{\rm spike})r^3_{\rm spike}\log\left(\frac{r_{\rm spike}}{r_{\rm ann}}\right),\, {\rm SIDM} \\
\rho^2(r_{\rm spike})r^3_{\rm ann}\frac{3}{5}\left(\frac{r_{\rm spike}}{r_{\rm ann}}\right)^{14/3},\, {\rm CDM}
\end{cases}
\end{equation}
The annihilation radius can be calculated as $r_{\rm ann}=[\left<\sigma_{\rm ann}v\right>t_{\rm age}\rho(r_{\rm spike})/m_\chi]^{1/\gamma}r_{\rm spike}$.

For a given dark matter mass, black hole mass and annihilation cross section, we can calculate the expected signal flux by integrating Eqs.~\ref{eq:halo} and~\ref{eq:spike} for $100~{\rm MeV}\leq E\leq100~{\rm GeV}$, the energy range of the Fermi-LAT gamma-ray space telescope. We take the photon spectrum $dN/dE$ from~\cite{Cirelli:2010xx}, and obtain the total flux as $\Phi_{\rm{total}}=\Phi_{\rm{halo}}+\Phi_{\rm{spike}}$. For $b\bar{b}$ final states, the upper limit on the gamma-ray flux is $\Phi_{\rm upper}\approx(62\textup{--}5.8)\times10^{-11}~{\rm cm^{-2}s^{-1} }$ for $m_\chi=10~{\rm GeV}\textup{--}1~{\rm TeV}$~\cite{Wanders:2014xia}, based on Fermi-LAT data on Draco. We vary the black hole mass and the dark matter mass, and derive upper limits on the annihilation cross section for the SIDM and CDM halo models of Draco.

The right panel of Fig.~\ref{fig:draco} shows the upper limits on the annihilation cross section  vs. the black hole mass for the SIDM (red) and CDM (black) halos, where we consider the dark matter mass $m_\chi=10~{\rm GeV}$ (dashed) and $1~{\rm TeV}$ (solid). The gray horizontal line denotes the canonical thermal cross section $\left<\sigma_{\rm ann}v\right>=3\times10^{-26}~{\rm cm^3/s}$. For the CDM halo, the thermal relic dark matter is excluded for $m_\chi=10~{\rm GeV}$ and $1~{\rm TeV}$ if $M_\bullet\gtrsim10~{\rm M_\odot}$ and $10^3~{\rm M_\odot}$, respectively. For the SIDM halo, the upper limits on the annihilation cross section are essentially independent of the black hole mass, and the constraints are significantly relaxed. Since both halo models have similar $\bar{J}$ factors for the smooth component, the difference in the $M_\bullet$ bounds is caused by their different spike profiles. Observationally, it's unknown whether Draco has a massive central black hole. If we extrapolate the black hole-host galaxy relation~\cite{Tremaine:2002js} to Draco, it could host a black hole with $M_\bullet\sim600~{\rm M_\odot}$. In this case, SIDM could be composed of thermal relics, but CDM could not for $m_\chi\lesssim1~{\rm TeV}$. In the limit where the spike is negligible, our analysis shows thermal relic dark matter is allowed for both halo models with $m_\chi\sim10~{\rm GeV}$. Ref.~\cite{Wanders:2014xia} finds a stronger limit of $m_\chi\gtrsim30~{\rm GeV}$ for a CDM halo. This is because it considers a density profile with $\bar{J}\approx1.20\times10^{19}~{\rm GeV^2/cm^5}$, which is a factor of $2.5$ higher than our case.

We have shown that SIDM thermalization leads to a weaker density spike near a central black hole. For the satellite galaxies like Draco, the presence of such a spike does not strengthen constraints on the SIDM annihilation cross section unless the black hole mass is much larger than $10^7~{\rm M_\odot}$, which is impossible for those systems given their small masses. As estimated in~\cite{Sameie:2019zfo}, the halo mass of Draco is about $2\times10^8~{\rm M_\odot}$ with a $4\times10^{9}~{\rm M_\odot}$ progenitor falling into the tidal field of the Milky Way. For the Milky Way itself, the central black hole mass is $4\times10^6~{\rm M_\odot}$~\cite{Gillessen:2008qv,Ghez:2008ms}. We have checked that the Milky Way's central black hole is not heavy enough to increase the signal strength for an SIDM halo. Thus, overall SIDM is less constrained than CDM in the search for annihilation signals from density spikes induced by central black holes. In this work, we focus on dark matter annihilations to $b\bar{b}$, as it is one of the most studied channels in dark matter indirect detection, but it's straightforward to extend to other channels as well. In addition, we could interpret our results in terms of a specific particle physics model of SIDM, combining with other constraints, see. e.g.,~\cite{Tulin:2013teo,Kaplinghat:2015gha,Bringmann:2016din,Cirelli:2016rnw,Chu:2016pew,Kamada:2018kmi,Chu:2018fzy,Bernal:2019uqr,Kang:2020yul}.

It is also interesting to note that Draco was considered as a challenging case for SIDM~\cite{Valli:2017ktb,Read:2018pft} as it has the highest dark matter content among the Milky Way satellites, but both dark matter self-interactions and tidal interactions are commonly expected to produce a shallow density core for a satellite galaxy. Recent works show the interplay of the two effects could actually lead to an opposite consequence, resulting in a high central density, due to the onset of SIDM core collapse~\cite{Nishikawa:2019lsc,Sameie:2019zfo,Kahlhoefer:2019oyt,Correa:2020qam,Turner:2020vlf}. Ref.~\cite{Sameie:2019zfo} uses N-body simulations and demonstrates that the isothermal density profile of Draco shown in the left panel of Fig.~\ref{fig:draco} can be produced in SIDM. If a halo is in the core-collapse phase, the inner dark matter velocity dispersion profile has a negative gradient and it's generally no longer a constant over the radius. Fortunately, for Draco, a mild collapse is enough and the inner velocity dispersion is approximately a constant~\cite{Sameie:2019zfo}. Thus our isothermal assumption is further justified. The upper limits on the annihilation cross section shown in the right panel of Fig.~\ref{fig:draco} are almost the same for the CDM and collapsed SIDM halo profiles.

\section{Implications for M87}

Lastly, we consider the supergiant elliptical galaxy M87, which hosts a central black hole mass with $M_{\bullet}\sim6.5\times10^9~{\rm M_\odot}$~\cite{Gebhardt:2009cr,Akiyama:2019eap}. Such a massive black hole could significantly enhance the spike density and boost indirect detection signals accordingly. Ref.~\cite{Lacroix:2015lxa} assumes a spike with $\rho(r)\propto r^{-7/3}$, and derives upper limits on the annihilation cross section to $b\bar{b}$ as $\left<\sigma_{\rm ann} v\right>\lesssim6\times10^{-30}\textup{--}10^{-26}~{\rm cm^3/s}$ for the dark matter mass in a range of $m_\chi\approx10~{\rm GeV}\textup{--}100~{\rm TeV}$. Thus, for CDM, thermal relic dark matter has been excluded for the entire mass range. For comparison, if the inner halo keeps an NFW profile of $\rho(r)\propto r^{-1}$, $\left<\sigma_{\rm ann} v\right>\lesssim8\times10^{-25}\textup{--}2\times10^{-21}~{\rm cm^3/s}$ for the same mass range~\cite{Lacroix:2015lxa}.

To estimate the limits for an SIDM halo, we take the dark matter density profile of M87 for $r\geq r_{\rm spike}\approx200~{\rm pc}$ shown in Fig. 1 of~\cite{Lacroix:2015lxa} and match it with the isothermal spike $\rho(r)\propto r^{-3/2}$ for $r<200~{\rm pc}$. We then calculate the $Q$ factor given in Eq.~\ref{eq:qfactor} for the SIDM spike and find it is a factor of $\sim10$ larger than the one with the NFW profile. Since $Q$ is insensitive to the annihilation radius in this case, we expect the SIDM limits could be stronger than the NFW ones by one order magnitude, i.e., $\left<\sigma_{\rm ann} v\right>\lesssim 10^{-25}\textup{--}10^{-22}~{\rm cm^3/s}$ for $m_\chi\approx10~{\rm GeV}\textup{--}100~{\rm TeV}$. It's important to note that dark matter self-interactions do not produce a shallow density core for M87. Unlike Draco, the luminous mass dominates the inner regions of M87~\cite{Gebhardt:2009cr} and SIDM thermalization with a deep baryonic potential could lead to a high density with a negligible core size~\cite{Kaplinghat:2013xca}, as dense as an NFW halo; see Fig. 6 of~\cite{Sameie:2018chj} for an example of the Milky Way. Thus, our recasting method is justified.

Another exciting aspect about the M87 target is that the Event Horizon Telescope (EHT) could resolve the dark matter density profile near the hole, due to its unprecedented angular resolution. Ref.~\cite{Lacroix:2016qpq} shows the EHT is sensitive to synchrotron emission induced by dark matter annihilations and the radiation from the annihilations could further enhance the photon ring around the shadow of the black hole. For a CDM spike with the $b\bar{b}$ channel, it shows $\left<\sigma_{\rm ann}v\right>\lesssim 3\times10^{-31}$ for $m_\chi\approx10~{\rm GeV}$, based on previous data releases from the EHT collaboration \cite{Doeleman:2012zc,Akiyama:2015qta}. We estimate the EHT sensitivity as $\left<\sigma_{\rm ann}v\right>\lesssim 10^{-26}~{\rm cm^2/s}$ with $m_\chi\approx10~{\rm GeV}$ for an SIDM spike. Thus, the EHT provides a unique probe of the thermal relic scenario of SIDM for light dark matter. Recently, the EHT collaboration observed the black hole shadow of M87 for the first time~\cite{Akiyama:2019eap}. It would be of great interest to take their new results and further test the nature of dark matter, which we leave for future work.

\section{Conclusions}

Dark matter self-interactions can thermalize the inner halo, resulting in an isothermal dark matter distribution. In this work, we have derived a dark matter density profile for an isothermal halo in the presence of a central black hole. The analytical model that we use is expected to be valid in the weak gravitational limit and in a region where the black hole mass dominates the gravitational potential of the inner halo. From the density profile, we extracted a spike power law of $r^{-3/2}$, which is much shallower than the one expected for CDM, i.e., $r^{-7/3}$. If dark matter annihilates, the density further exhibits an annihilation cusp with a power law of $r^{-1/2}$ in the inner region where the annihilation could occur within the age of the halo. We constructed spike profiles for the satellite galaxy Draco, and studied indirect detection constraints on the annihilation cross section and the central black hole mass using the Fermi-LAT gamma-ray data. For an isothermal halo as predicted in SIDM, the upper limits on the cross section is not sensitive to the presence of a density spike, if the black hole mass is reasonable for the system we consider. In contrast, for CDM, the possibility of an existing intermediate black hole in Draco has been excluded for thermal relic dark matter, as it predicts a steeper density spike. Overall, SIDM is less constrained than standard CDM in searches for dark matter annihilations from the density spikes. In the future, it would be interesting to extend our analysis to massive elliptical galaxies containing supermassive black holes, such as M87. In addition, we could study the distribution of SIDM particles near a black hole in the strong gravitational limit, which might be important for understanding growth of supermassive black holes in the early Universe, see., e.g.,~\cite{Balberg:2001qg,Feng:2020kxv,Choquette:2018lvq}.

\acknowledgments
We thank Omid Sameie and Mauro Valli for providing data on density profiles for Draco. HBY was supported by U.S. Department of Energy under Grant No. de-sc0008541, NASA 80NSSC20K0566, and the John Templeton Foundation \#61884.

redpajama_set_name: RedPajamaArXiv


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How trustworthy is the iPhone alarm clock?
Discussion in 'iPhone' started by wadawow, Aug 14, 2011.
I need a dock and wondering if I should get an alarm/dock combo or just a dock... is it pretty reliable?
I sometimes find that I swipe instead of hit snooze on the screen when I'm zombie like but that might be just me.
I invested in an old school alarm.
Hasn't let me down once.
The iPhone alarm clock is one of the reasons why I must have my iPhone. I have a bad memory and i use the alarm clock to remind me to do things during the week. I tend to hit the snooze button alot, and this alarm clock will pester you a hundred times until you end the alarm. Much more reliable than other phones.
The only thing to be wary about is when daylight savings time begins or ends.
Seems like Apple has screwed this up every year since the iPhone began.
I think this most recent daylight savings was the first one that wasn't effected by some bug or an other.
I use it daily. Going on 3+ years as my morning alarm without any problems.
I've never had a problem with my iPhone's alarm.
If you jailbreak, it's not at all.
works as good as any other alarm clock.
I have some that are set for work Mon-Fri and they've yet to fail to go off. That's actually better than the Sony alarm clock I have on my night stand.
exactly, it's the same here.
I use it as my only alarm clock. Has worked perfectly for the last 4 years for me.
I found the alarm to be 100% reliable - so far.
If you don't want to mess with the snooze (I hate that second wake-up, the first time is bad enough ) - turn it off.
Also, I find the timer very useful.
Well I used it for over two years and it was 100% reliable. But I recently got a basic digital alarm clock for beside my bed so that I can keep my phone in my office so I can sleep better. So I'm no longer using it anymore. Still the best phone alarm clock I've ever used.
I'm a postman who gets up at 4:30am so I need an alarm that's reliable.
I've never been let down by my iPhone alarm yet.
100% reliability for me so far, but as noted probably hundreds of thousands have suffered DST bugs.
iPhone Alarm clock is reliable and has multiple alarms but it is not the easiest to use. I hate digging thru menus to turn an alarm on or off.
Beautiful Clock Radio is much easier to set, turn on and off and has better sounds and is a nice clock and radio. if you care about that.


And make me a sammich.
NEW YORK (AP) - NEW YORK - A finger-pointing political argument on Fox News Channel boiled over when a male conservative talk show host told a woman to "know your role and shut your mouth."
I guess that's why I don't watch much TV. It's been corrupted by stupidity.
If he'd have said that to my wife, he wouldn't have any front teefus left.
I'm glad somebody told her that; she's got too much to say about everything, all of it ignorant.
Damn. I need to watch more TV. I didn't know she'd earned it.
She was defending her unrelated namesake...Eric Holder.
She always hijacks the point that Hanity is trying to make. I really hate it when she is on his show, she has no manners and feels free to talk over anyone who is presenting a point of view that she does not agree with. I wish that the hosts had the ability to just shut off their mike when they start the filibustering.
Did I miss some reality TV drama, known at Fox News, last night?
Yes, know your place. Shut up and just give me the news.
It's that "fair & balanced" bullsh*t...purposely hamstringing yourself is a sure sign of weakness and stupidity.
And good thing I am not on TV...it wouldn't last long...turning off a mike won't cut it for me...making the offender cry and run off the set is the least I would want to do...strangling them with my bare hands would be a quick second.


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I am sure photographers do processing and I think there is nothing wrong in it until you start altering the facts in a photo. I recently started learning this great tool (Adobe Lightroom). Here are few old photos post processed in Lightroom.


text:
Q: Can I use Prometheus to list the files processing or already processed? I need to know the time per service of an application, which is processing some files. So I mean: the same file passes through each service and I need to know each pipeline time. Is that possible with Prometheus and, for example, Grafana? Or there is another tool for it? Or even... do I need to implement it on my own? (Obs: the services run in Python)

A: Well, it is very broad question, and can be answered only broadly. I'm sure the community here would ask you to go through this before posting a question: How to Ask

From what I understand from the question, what is being looked for is custom metrics. Prometheus is widely used for gathering metrics. You can use a library like prometheus_client and instrument the time taken to process the files in each stage.
If the services that process the files are not batch jobs or cronjobs and can expose API endpoints, expose the metrics on, for example, "/metrics". This is only the publishing part. The metrics endpoint can then be consumed by Prometheus service using its scrape_config configurations. Read more about it here.
If the services cannot expose endpoints and hence metrics, they can "push" the metrics to a Prometheus Push Gateway, and Prometheus can be configured to scrape the gateway. Read more about it here.
It also has to be noted that it will not be advisable to try and publish metrics per file. The general practice is to publish metrics per file type.
Once all the metrics are available in Prometheus, Grafana can then read from Prometheus and display graphs.
There are a myriad of other architectural decisions one may need to take while setting it all up, but it is quite broad to be covered here. Hope this answer quickly provides you some references. Happy monitoring!

redpajama_set_name: RedPajamaStackExchange


text:
Tarell Brown plays the game, and lives his life, for those he's lost
Mark Daniels Journal Sports Writer MarkDanielsPJ
FOXBORO – The boy stepped out on the field, in mourning. He did all he could to hold back the tears.
With each snap, he ran, hit and pushed harder. This was his outlet; his sanctuary. These were the moments that made him feel normal in a time when not much else did. Football was a distraction. It was his salvation.
Tarell Brown was 10 years old when his mother, Tonya Edmonds, was murdered outside their Texas home. A week later, he strapped on his pads and turned to football for an escape. Twenty years later, he's doing the same thing.
"This is my outlet. Football helps me get away from the real world," Brown said. "It definitely keeps my mind at ease. This is the only place that I'm kind of comfortable at on a day-to-day basis. It definitely helps me."
He'll never forget that morning – Aug. 2, 1995 - or the games that followed. Athletics were already a big part of Brown's life. He played soccer, basketball and baseball, but loved football. And now, he needed it more than ever.
His father, Robert Brown, wanted to keep his son busy in a time of sorrow, so Tarell suited up and played. He scored four touchdowns that day.
"I think it was like a week later. He was a little soldier," said Tarell Brown's stepmother, Demetra Brown. "That's how I described it. He just kind of marched on through. He's always been that way. Just like a little soldier. He never let it get him down. He didn't let it stop him. It could have. It could have broke him. It could've been the thing that made him become self-destructive. But it didn't. It made him more determined. I think it was his saving grace."
"We didn't baby him," added his grandmother, Bonita Brown. "We encouraged him. 'You have to be strong. This is what your mother wanted.'"
He wanted to make his mother proud. She was always his biggest cheerleader. So when he took the field that day he felt free. In what was supposed to be a way for the boy to cope, there were moments he felt closer to her.
"I think, he could kind of be with her in a way," Demetra Brown said. "I think he kind of always knew that she was there, kind of watching over him. I do believe sports helped save him."
It wouldn't be the last time.
TONYA EDMONDS had already made her son's lunch for school when she left the house that morning.
Tarell Brown was asleep at the time. His alarm for school was set, but he was awakened by police officers instead. They spared him the details as they led him outside.
A secretary at the Federal Deposit Insurance Corporation in Dallas, Edmonds had walked to her car, which was parked behind their house right on the border separating Balch Springs and Mesquite, Texas. It was around 6:30 a.m. when the assailant approached her on Park Hill Circle, a stone's throw from where her son was sleeping. Neighbors heard a single shot. Edmonds' killer was never found.
Brown moved in with his father and stepmother, went to counseling as a child and continued to play football. It was hard to be a normal kid after that, but the family did their best. Robert Brown taught his son about the game of football.
"He was the one who helped motivate me, get me through. He definitely pushed me," Tarell Brown said. "I feel like if it wasn't for him, I wouldn't be where I am today. He definitely was a motivator, but also a man of character."
But his father would never see the payoff.
Robert Brown, who had sickle-cell disease, died of a heart attack on Feb. 14, 2007 – two and half months before the cornerback was drafted by the San Francisco 49ers, out of the University of Texas. His grandmother and other family members offered up similar advice.
"You've got to be strong because this is what they worked for, Tarell," Bonita Brown said. "Things like that. He knew it. Everything just flows out of him now. All the wisdom. He just never gave up."
The memory of his mom and dad is not just what he plays for. It's what he lives for. His grandmother sees it. He has the same mannerisms as his father, Robert: cool, calm and collected. But perhaps the biggest thing he learned from his parents was determination.
"His mother, she was always striving to do better," Bonita Brown said. "She was always in this class and that class, and studying for this and that. She was always trying to strive. My son was always the same way. Along the way he determined that, 'My parents instilled this in me.' They always strived. It was just inbred in him. Keep going. No matter what."
ROBERT BROWN was in the hospital when the doctors told him he had to stay the night.
The father and Dallas-area bus driver did all he could for his son without letting sickle-cell disease hold him back. If that meant defying doctor's orders, so be it. There was no way this man was going to miss his son's game. He was going to be there every chance he could.
"He was in the hospital and they were like, 'You can't go home today,'" Demetra Brown said. "He was like, 'What do you mean I can't go home today? I have a football game I have to coach. I'm going home.'"
As Tarell Brown saw time and again, his father was a fighter.
"He gets that from his dad," Demetra added. "You've got to get up. You've got to march on."
Duane Akina saw that firsthand.
The former Texas defensive coordinator and defensive backs coach watched his cornerback fight through physical and emotional pain during his time as a Longhorn. Brown's senior season was viewed by scouts as a disappointment.
Early that season, Brown suffered a hairline fracture in his left toe against Oklahoma, and played out the remaining seven games at less than full strength. The team trainer had to cut his cleat in order to relieve the pressure from swelling.
"He had the broken toe his senior year. He wasn't having the year we all anticipated. He was playing on one leg," Akina said. "He has continued to overcome situations on the field, off the field, at a young age and here moving into the tail end of his career. He keeps turning negatives into positives."
A ROAD MAP OF PAIN is printed all over Brown's body. Tattoos fill up his arms, hands, chest and back. They tell his life's story.
He has a warrior princess on his left arm, in honor of his mother. Roses for both his parents on his forearm and an image of them on his back. His three daughters' names – Takyla, Tariah and Isabella – are etched into his skin. Other people he has lost are also memorialized forever on Brown's body.
"I think it motivates me every day. It just makes me a stronger and tougher person," Brown said. "I think going through those day-to-day battles and going through all the stuff that I went through in my life made me the man I am today. Makes me a tough-skinned guy. Somebody that's able to endure a lot, but at the same time can fight back. That's a testament of me of just growing up in a harsh environment."
Brown didn't have what anyone would call a normal childhood. He tries to make up for that now, by providing for children in Mesquite, Texas.
Every summer, the cornerback and his Brown's Kids Foundation put on a free football and cheerleading skills clinic. He's given away backpacks and free dinners on Christmas and Thanksgiving.
He's done so much, every June 25 is now known as Tarell Brown Day in Mesquite. Brown continues to work hard in memory of his parents.
"What I do day-in and day-out is to prove other people wrong, too," Brown said. "And to let other kids know that just because tragic things can happen in your life, doesn't mean that you have to stop. It doesn't mean that you can't still achieve all your goals."
"He does so much to give back," added Steve Bragg, Brown's coach at North Mesquite High School. "Tarell remembers where he came from and what it was like. His family didn't have a whole lot.
"The kid has been through so much. Losing his mom and then losing his dad when he was at Texas. I definitely think football and athletics is his outlet. It's his life. It's his identity."
Those early struggles molded him into who he is today with the Patriots. The lessons helped him during a time like this past offseason, when he was unsigned and rehabbing a broken foot. In a lot of ways he's still that 10-year-old boy who held back the tears to play football 20 years ago.
"I've been a fighter my whole life. That's all I know is to fight," Brown said. "My back has been against and in the corner for a long time. I understand what it's like to battle not only adversity, but battle life. So to fight through that, that's what I'm here to do. That's why I always say, I'm built to last."
"He's a survivor. Put it that way," Bonita Brown said. "He's really a survivor."
Like his father, Robert. Always determined. Or perhaps it's like his mother, Tonya. Always striving.
Tarell Brown marches on.

redpajama_set_name: RedPajamaCommonCrawl


Advantech WebAccess SCADA version 8.3.2 suffers from a code execution vulnerability.
# 1) CVE-2018-15707 to steal credentials (XSS). User-interaction required.
# 2) CVE-2018-15705 to write an ASP file to the server.
print "\n'" + filename + "' written to disk."
print "\nSuccessful request to '" + url + "'\n"
print "\nThere may be something wrong with the ASP payload.\n"
desc = '''This exploit targets Advantech WebAccess/SCADA 8.3.2. It has been tested against Windows 2008 R2 x64.
The goal of the script is to execute code remotely. User interaction is required.
3) Ensure user-specified project exists.
4) Ensure user-specified node exists.
6) Start HTTP listener to receive credentials when victim clicks the link.
Note: elevated privileges will be obtained using the Webdraw RemoteWinExec function.
print "\nError: IP Address is invalid: '" + ip + "'.\n"
print "\nPerforming some banner checks to ensure services are running...\n"
print "Dashboard Viewer is up."
print "Specified project '" + victim['project'] + "' exists."
print "Specified node '" + victim['node'] + "' exists."
print "\nSend this link to the victim:"
print "Keep in mind, they could be logged in via localhost."
print "Waiting for victim to click link..."


text:
A Man With Yellow Armpitsresource center
What's Your Diagnosis?
A Man With Yellow Armpits
Volume 59 - Issue 4 - April 2019
For "Irritant Contact Dermatitis Caused by Hand Sanitizer Use and Handwashing During the COVID-19 Pandemic," click here
Peggy R. Cyr, MD
Family Medicine Physician, Maine Medical Center, Portland, Maine
Leigh P. Johnson, MD
Internal Medicine Resident, Virginia Commonwealth University Health System, Richmond, Virginia
Christina E. Finch, MD
Family Medicine Resident, Kaiser Permanente, San Diego, California
Cyr PR, Johnson LP, Finch CE. A man with yellow armpits. Consultant. 2019;59(4):111-112, 128.
A 48-year-old man presented to his primary care office with numerous firm yellow nodules attached to his armpit hairs for several weeks (Figure). He denied pain or pruritus; however, a new foul smell had developed that did not improve with showering or the use of deodorant. The armpits of his shirts had become stained yellow.
What's Your Diagnosis?
A. Piedra
B. Hair casts
C. Trichomycosis axillaris
D. Pediculosis
E. Erythrasma
ANSWER: Trichomycosis axillaris
Based on the patient's history and the clinical appearance, he received a diagnosis of trichomycosis axillaris.
Trichomycosis axillaris is a superficial bacterial infection involving nodular, insoluble concretions that encircle axillary hair shafts. The name of the condition is a misnomer because there is no fungal involvement; it has been better described in the literature as trichobacteriosis or bacterial trichonodosis. Bacteria from the genus Corynebacterium secrete a hard substance that creates an immobile, beaded material.1 The secretion can be yellow, as in our patient's case, or black or red, with the differences in color thought to likely be caused by infection with different Corynebacterium species.1
Men are more commonly affected than women due to cultural hair-removal customs, and most cases occur in humid or tropical climates. Most patients present with axillary symptoms, although the infection can occur in other areas such as the pubic area or intergluteal area. The infection can be transmitted to others through very close contact. Patients often experience an associated increase in sweating, changes in hair texture, or a foul odor. The infection is otherwise asymptomatic and is likely underreported and underdiagnosed due to its relatively mild symptomatology.1
Trichomycosis can be detected under a Wood lamp and by way of microbiological tests, but empirical treatment is often a reasonable first step when the condition is suspected. First-line management includes antimicrobial soap, benzoyl peroxide wash, topical erythromycin, and shaving of the affected hairs for a few weeks. Topical antimycotic agents have been shown to be effective, and oral erythromycin is indicated in severe cases.2
The differential diagnosis includes piedra, hair casts, pediculosis, and erythrasma. Dermoscopy can be useful in differentiating abnormalities of skin, follicular, and hair shaft abnormalities.
Piedra is an infection with the fungus Trichosporon beigelii and is characterized by white (soft and gelatinous) or black (firm) concretions on the hair shafts, usually of the scalp. Unlike trichomycosis, piedra nodules can be easily separated from the hair, and hair shaft breakage is common.3,4
Hair casts are parakeratotic scales, made up of desquamated epithelial cell plugs, that encircle hair follicles. Unlike trichomycosis, hair cast concretions are mobile along the involved hair shaft and often occur in patients with psoriasis or seborrheic dermatitis.3,5
Pediculosis is a parasitic infection with blood-feeding lice. The body louse attaches its eggs to clothes, the head louse attaches eggs to hair follicles, and the crab louse attaches eggs mainly to pubic hairs. Early stages of trichomycosis can sometimes be confused with pediculosis, given that the discrete nodules appear and feel similar to nits, but as pediculosis becomes chronic, the concretions lengthen, creating a sheath along the hair shaft, and often deepen in color. All lice infections are contagious and very pruritic due to hypersensitivity reaction from lice saliva, unlike trichomycosis, which typically causes little discomfort.6
Erythrasma is similar to trichomycosis in that it is also caused by a Corynebacterium species—specifically Corynebacterium minutissimum. Erythrasma often affects persons with diabetes and persons who are obese. It is characterized by nonpruritic, pink and brown, scaly skin patches, typically in skin folds.7
OUTCOME OF THE CASE
The patient was successfully treated with 2 weeks of the synergistic approach of shaving his armpit hair 3 times per week, using an antimicrobial body wash daily, and applying topical erythromycin daily. His symptoms fully resolved and had not recurred at a 1-month follow-up visit.
Bonifaz A, Váquez-González D, Fierro L, Araiza J, Ponce RM. Trichomycosis (trichobacteriosis): clinical and microbiological experience with 56 cases. Int J Trichology. 2013;5(1):12-16.
Zhao Z, Ma L. Skin and soft tissue infections: a clinical overview. In: Tang Y-W, Sussman M, Liu D, Poxton I, Schwartzman J, eds. Molecular Medical Microbiology. Vol 2nd ed. New York, NY: Academic Press; 2015:825-835.
Prado R, High WA, Bernhard JD, et al. Trichomycosis axillaris – skin. visualDx. https://www.visualdx.com/visualdx/diagnosis/trichomycosis+axillaris?moduleId=7&diagnosisId=52430. Updated January 23, 2015. Accessed March 11, 2019.
Hay RJ, Ashbee HR. Fungal infections. In: Griffiths CEM, Barker J, Bleiker T, Chalmers R, Creamer D, eds. Rook's Textbook of Dermatology. Vol 1. 8th ed. Hoboken, NJ: Wiley-Blackwell; 2016:chap 32.
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Nuwara Eliya Travel Guide Nuwara Eliya Trips Nuwara Eliya: Guide To The Hidden Mountain Town In Sri Lanka
Nuwara Eliya: Guide To The Hidden Mountain Town In Sri Lanka
By Pallavi Paul
When we think of Sri Lanka, we instantly envision sun-kissed beaches, waves lapping against sandy shores and cute coastal towns. Our mind certainly doesn't conjure an image of us sitting in a light sweater, sipping on piping hot chai in a lush mountain city, does it?Well, it should. Say hello to Nuwara Eliya – a proof of the versatility of Sri Lanka's unique terrain. Besides being one of the most important locations for tea production, this vibrant, bustling city is also a popular tourist haunt.
Why travel to Nuwara Eliya?
La Grande Villa
King Fern Cottage
Credits: cat_collector
With its cool climate, lush landscape and natural beauty. Nuwara Eliya is an undoubted paradise for travellers. If you like nature you can go visit the many parks and botanical gardens it has to offer, visit serene Buddhist temples, explore the tea plantations, trek your way up to Lover's Leap waterfall or even go on a shopping tour!
Cuisines on offer
Credits: Wikimedia Commons
If you love food, Nuwara Eliya is a must-visit. Having a wide variety of vegetarian as well as non vegetarian options, this mountain town is an absolute paradise for foodies. From the insanely popular kottu (chopped roti mixed with vegetables, chicken and egg) to polos (Jackfruit curry), there is something for everyone. A great place for local food is Indian Summer Nuwara Eliya. Apart from authentic Sri Lankan cuisine you can also try out Queenswood Restaurant (Asian cuisine), Grand Thai (Thai cuisine) and Salmiya (Italian cuisine).
Getting a Sri Lankan Tourist Visa is super simple for Indians and the process is extremely efficient. You don't need to visit the embassy and can apply for the visa online. You will then be issued an ETA (Electronic Travel Authorisation) within 45 minutes to 1 hour of your application! This allows you to enter the country for the next 30 days.
Weather at Nuwara Eliya is pleasant all year round with the average temperature hovering around 16 degree Celsius and the highest temperature hitting 30 degree Celsius. If you are looking forward to moderate climate, February to April is the best time to go. The Sinhalese New Year is also celebrated in the month of April, so this is a perfect time to visit if you wish to catch the vibrancy and festivities.
Since there is no direct connectivity from New Delhi to Nuwara Eliya, you have to first fly to Colombo. There are several direct and connecting flights from New Delhi's Indira Gandhi International Airport to Bandaranaike International Airport in Colombo.
Train: You can reach Nuwara Eliya from Nanu Oya which falls on the Colombo-Kandy route. A second class ticket from Colombo costs about ₹100. Once you get off at the Nanu Oya station you can hire a cab or take a bus to Nuwara Eliya. The journey takes a total of 5-6 hours.
Road: You can also jump abroad a local bus from Colombo to Nuwara Eliya (which may take longer, as buses are usually slower) or hire a private cab. The travel time is around 5 to 5.5 hours.
Since Nuwara Eliya is a small town most places are within close proximity. You can easily hire a tuk-tuk to sight see and get around . A ride may cost you anywhere between ₹200 to ₹600 - it essentially depends on where you are headed. The rates are usually higher at night.
Flight from New Delhi to Colombo: ₹16,000
One-way ticket on local transport: ₹250
Taxi starting tariff: ₹50
Hotel stay in Nuwara Eliya: ₹3,000
A meal: ₹800 approx. (meal for 2 in a mid-range restaurant)
Luxury stay:
Cost: ₹20,280 per night (breakfast included)
Mid-range stay:
Cost: ₹2,533 per night (breakfast included)
Budget stay:
Trout Cabines
For more hotel options in Nuwara Eliya go here.
Have you been to Nuwara Eliya before? What did you explore there? Share your experience with Tripoto and help a growing community of travellers plan their next trip!
You can also check out Tripoto's YouTube channel for some fun travel videos.
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